Crayfish population size under different routes of pathogen transmission

Abstract We present an epidemiological model for the crayfish plague, a disease caused by an invasive oomycete Aphanomyces astaci, and its general susceptible freshwater crayfish host. The pathogen shows high virulence with resulting high mortality rates in freshwater crayfishes native to Europe, Asia, Australia, and South America. The crayfish plague occurrence shows complicated dynamics due to the several types of possible infection routes, which include cannibalism and necrophagy. We explore this complexity by addressing the roles of host cannibalism and the multiple routes of transmission through (1) environment, (2) contact, (3) cannibalism, and (4) scavenging of infected carcasses. We describe a compartment model having six classes of crayfish and a pool of crayfish plague spores from a single nonevolving strain. We show that environmental transmission is the decisive factor in the development of epidemics. Compared with a pathogen‐free crayfish population, the presence of the pathogen with a low environmental transmission rate, regardless of the contact transmission rate, decreases the crayfish population size with a low risk of extinction. Conversely, a high transmission rate could drive both the crayfish and pathogen populations to extinction. High contact transmission rate with a low but nonzero environmental transmission rate can have mixed outcomes from extinction to large healthy population, depending on the initial values. Scavenging and cannibalism have a relevant role only when the environmental transmission rate is low, but scavenging can destabilize the system by transmitting the pathogen from a dead to a susceptible host. To the contrary, cannibalism stabilizes the dynamics by decreasing the proportion of infected population. Our model provides a simple tool for further analysis of complex host parasite dynamics and for the general understanding of crayfish disease dynamics in the wild.


| INTRODUC TI ON
Pathogens and their hosts are tied together. Given enough time, those pairs that can coexist thrive, while the others disappear through extinction of either the host or the pathogen. An introduction of a novel pathogen to an established ecosystem may bring forth rapid changes in the population dynamics of the naïve hosts. If the pathogen can spread efficiently even within a sparse host population, for example through water, the effects are even stronger.
Such an invasion of a pathogen may be disastrous for most host populations, as has been in the case of the oomycete Aphanomyces astaci, causing deadly crayfish plague in the European noble crayfish (Astacus astacus; Makkonen et al., 2018;Martín-Torrijos et al., 2021;Svoboda et al., 2017).
While crayfishes are generalists with occasionally high biomass (Reynolds et al., 2013), their population dynamics are complex and affected by a multitude of mechanisms. Crayfishes, often considered keystone species, show ontogenetic and seasonal niche shifts (Abrahamsson, 1966;Guan & Wiles, 1998) and act as ecosystem engineers by digging burrows and clearing aquatic vegetation (Abrahamsson, 1966;Dorn & Mittelbach, 1999;Statzner et al., 2000;Thomas & Taylor, 2013). Importantly, crayfish scavenge a wide range of dead animals including conspecifics and other crayfishes (Guan & Wiles, 1998;Houghton et al., 2017). Scavenging can increase per capita resource availability by widening the potential scope of food items (Boros et al., 2020), but crayfish also commonly show cannibalism at high population densities (Guan & Wiles, 1998;He et al., 2021;Houghton et al., 2017). Cannibalism can efficiently regulate population growth and induce fluctuating dynamics both in the average size of individuals and in the population size in indeterminately growing organisms (Abrahamsson, 1966;Claessen et al., 2004;Houghton et al., 2017;Rudolf & Antonovics, 2007). The relative abundance of suitable refugees affects the susceptibility of crayfish to cannibalism at all ages (Guan & Wiles, 1998;Houghton et al., 2017). Crayfish are predated not only by larger conspecifics but also by numerous fishes, mammals and birds (Houghton et al., 2017;Reynolds et al., 2013), and large crayfish are harvested as part of freshwater fisheries or "crayfisheries". All these mechanisms challenge the development of simple population models for crayfishes, while such models would be needed for the sustainable management of these species (Jones & Coulson, 2006;Todd et al., 2018;Whiterod et al., 2020).
A major complication to the modeling of crayfish population dynamics arises from their diseases that can cause both chronic sublethal fitness losses and acute, catastrophic population crashes.
Individuals weakened by diseases may be increasingly vulnerable to cannibalism, while dead individuals may be readily consumed. Both feeding habits can act as direct transmission routes for the pathogens and further complicate the epidemiological and population dynamical patterns in crayfish and their pathogen populations (e.g., Getz & Pickering, 1983;Kohler & Holland, 2001;Rudolf & Antonovics, 2007). Of all the known crayfish disease agents, oomycete A. astaci can be considered the most virulent (Makkonen et al., 2018;Martín-Torrijos et al., 2021;Svoboda et al., 2017). A. astaci originates from North America, where it coexists with its native host species such as signal crayfish Pacifastacus leniusculus. The crayfish plague manifests in physiological and behavioral changes, progressive paralyzation, and ultimately death, but the disease severity may vary significantly among host species with native host species being able to live even several years with the pathogen (Jussila et al., 2021;Oidtmann et al., 2002). Crayfish infected with A. astaci spread the pathogen by carrying the oomycete mycelium in their cuticle. The mycelium releases the infective zoospores to the water (Oidtmann et al., 2002). The number of zoospores that are released depends on the status of the infected crayfish. If the infection is latent, i.e., weak (asymptomatic), and when the crayfish has control over the pathogen, zoospore production remains low but may increase during molting (Strand et al., 2012). However, for a period that begins 1 week before the disease-induced death and continues some days after the death, the host zoospore production increases. Zoospores are initially distributed in water unequally so that the density is the highest close to the source host. Without significant turbulence, zoospores tend to remain near the bottom of the waterbody but use chemotaxis to find the crayfish (Oidtmann et al., 2002;Strand et al., 2012).
Carcasses of succumbed crayfish can remain infective several days after the death and release new zoospores into the environment.
Active zoospores have limited survival time outside host, but they can transform into resistant cysts that in turn can transform back to motile zoospores (Oidtmann et al., 2002;Unestam, 1969). The cysts have considerably longer lifespans than the active zoospores, surviving 2 weeks in distilled water (Unestam, 1969). Cold environment increases the survival of the spores, and a survival period of 2 months has been observed (Unestam, 1966).
Although there has been a great empirical interest in the epidemiology of crayfish plague and population dynamics of crayfish stocks, these dynamics have not been captured by developing host parasite models that would explicitly account for the various infection routes (Jussila et al., 2015;Strand et al., 2012). To formulate such a model, it is necessary to describe the transmission dynamics of the A. astaci. First, the spread of the plague in a naïve crayfish population may largely follow standard density-dependent transmission with the resulting fast population crash. However, under a certain threshold density, the pathogen transmission might follow a horizontal or vertical, frequency-dependent infection process regulated by the behavior of the crayfish (Svoboda et al., 2017).
Thus, transmission of the crayfish plague generally includes an environmental transmission component through the environmentally

T A X O N O M Y C L A S S I F I C A T I O N
Community ecology, Conservation ecology, Disease ecology, Invasion ecology, Population ecology, Theorectical ecology spreading spores emitted by the dead and alive infected crayfish (Oidtmann et al., 2002) and contact-aided transmissions with varying relative importance. Second, contacts conveying transmission may relate to aggressive and territorial behavior of crayfishes and to the scavenging of the deceased carcasses, a portion of which are infected with A. astaci. Cannibalism has been shown to be an important transmission route, for example, for the Yellow head virus in shrimp aquaculture (Hamano et al., 2015), but it is unclear, if cannibalism is a significant infection route in wild populations (Rudolf & Antonovics, 2007). The third impetus for the pathogen transmission comes through scavenging. Crayfish have been shown to eat infected pieces of conspecifics (Imhoff et al., 2012;Oidtmann et al., 2002). Therefore, the crayfish do not avoid the infected carcasses, but use them as a food source. The necrophagy increases the risk of transmission by two mechanisms. First, the crayfish are in close contact with the infected carcasses for a prolonged time.
Because A. astaci zoospore production is at highest right before and after the death of the infected individual, the effect of scavenging in pathogen transmission is likely notable for the scavenging individual.
Second, transmission through eating infected parts of conspecifics can result in higher pathogen concentration than transmission through environment, as shown for the microsporidian parasite infecting two freshwater host species by Imhoff et al. (2012). As a result, the most obvious transmission route for A. astaci remains the environment, but the possibility of significant contact transmissions cannot be ruled out.
The abovementioned infection routes are hereafter referred to as environmental transmission (Keeling & Rohani, 2002;Li et al., 2009), contact transmission (Keeling & Rohani, 2002), transmission through cannibalism (Rudolf & Antonovics, 2007), and transmission through scavenging (Oidtmann et al., 2002), according to the source of infection. The environmental transmission is considered as a density-dependent process, whereas the contact transmission, transmission through cannibalism, and transmission through scavenging are modeled as density and frequency-dependent processes.
The assumption behind this is the idea that the crayfish cannot tell apart the health status of their live or deceased conspecifics. A certain fraction of the cannibalized or otherwise contacted individuals and scavenged dead individuals are infectious leading to infection of a susceptible individual.
Because the zoospore density in the proximity of the susceptible hosts is the determinant biological route to infection, equal exposure may be obtained through various transmission routes, and the relative role of each transmission route may depend on host population density. For the disease transmission, on the other hand, the disease virulence is the most important trait as predicted by the classic trade-off model of disease virulence (Anderson & May, 1982).
However, due to the scavenging, high infection mortality does not prevent the infection from spreading. Therefore, the assumptions of the trade-off model do not hold (Anderson & May, 1982), and transmission is expected even to rare hosts via scavenging. These mechanisms are likely to cause highly labile population dynamics for which there is no standard population dynamical theory (Alizon et al., 2009). The present model is applicable to species that show relatively stable mortality rate throughout the life and across seasons (including A. astaci and similar species). For example, A. astacus has a lifespan of over 15 years, though the estimates vary greatly (Vogt, 2014). It generally grows slower and lives longer in higher latitudes and colder environments.
We focus here on the population dynamical consequences of the four transmission routes using a model with two host life stages that can both be susceptible or infected. We analyze the effects of different transmission routes on the long-term crayfish population density, which is measured as the corresponding mean value of the variable under consideration (because sometimes the system is cyclic, see Materials and Methods). We compare the environmental transmission to other transmission routes to uncover if some routes dominate the others and if they have a joint effect on the crayfish population. Moreover, we examine specifically if the transmissions through scavenging or cannibalism have an effect of the crayfish population size. We quantify the intensity of infection in the terms of incidence rate of the plague infections in the adult crayfish population. In this measure, the population sizes represent the susceptible and the infected adult crayfish populations. Our goal is to provide a generally applicable model of a fatal disease to assess the relative importance of different transmission routes in any structurally similar system with cannibalistic hosts.

| Model description
We consider here a simplified crayfish population with two life stages (juveniles and adults). Two behavioral patterns are characteristic for the crayfish in their acquisition of resources: (1) intraspecific predation (cannibalism) and (2) scavenging. The crayfish population is subject to a disease that has four transmission routes: (1) environmental transmission, (2) contact transmission, (3) transmission through cannibalism, and (4) transmission through scavenging carcasses of disease-killed individuals.
The density of the plague spores in the environment is denoted by P (Figure 1). The densities of susceptible juvenile and adult crayfish are denoted by J and S, respectively. M and I denote the densities of infected juvenile and adult crayfish. T and C denote the densities of the deceased uninfected and infected crayfish carcasses, respectively ( Figure 1).
The general model of the crayfish population dynamics, infected by the crayfish plague, is described by a set of differential equations as (1) The model includes several assumptions that may be important for some crayfishes or specific circumstances. In the spatial context, our model describes a closed population leaving out spatial structures and migrations. In the disease dynamics, we exclude fish and other potential vectors of transmission. We also assume that the disease has a constant virulence, i.e., represents a single nonevolving strain. In particular, we assume that the disease is fatal such that no recovery or immunization takes place. Globally, this leaves out a few North American crayfishes as hosts, but includes the rest. We assume that there is no explicit cannibalism within the young age class. We also assume that the young class individuals The crayfish and Aphanomyces astaci form a complex system with several connections. The crayfish population is regulated by the intraspecific predation, where susceptible adult crayfish (S) cannibalize the juveniles (J). Susceptible adults also consume the crayfish carcasses (T) for additional energy. Part of the energy thus gained can be used in reproduction. The oomycete grows in the infected juveniles (M), adults (I) and carcasses (C) producing infective spores (P). The susceptible juveniles are infected either through the water or through contact with infected conspecifics. Likewise, the susceptible adults can get an infection through water and through contact with infected conspecifics. Additionally, adults are at risk of getting infected through intraspecific predation and necrophagy. Infected carcasses lose their infectiveness at certain rate, transferring from (C) to (T). Both types of carcasses decay naturally. The blue circles signify the pathogen-free compartments in the model, whereas the red circles mark the pathogen affected compartments. Solid black lines show the direct development or reproduction of the individuals, and dotted red lines represent the infection transmission routes.
rely on environmental sources of food instead of scavenging conspecifics. The only way in which the population recruits is through the linear offspring production (Equation 2), and the only way the individuals are vanished from the system is through the decay of the uninfected (Equation 6) and infected carcasses (Equation 7).
When comparing the force of infection of the different transmission routes, we use the measure of incidence rate defined as follows: Incidence rate measures the rate of appearance of new cases in the group or population, i.e., the number of infected within a specified period of time related to the total number of individuals exposed to risk during that period (Olweus, 1989). We apply this measure using the adult crayfish as the target group such that the mean rates of infections of the adult crayfish population are calculated during the last 60,000 days of the simulation. Thus, the incidence rate of each transmission route becomes:

| Parameterization of the model
We apply the model on the noble crayfish. The parameters for crayfish population density, population structure, and fecundity were adapted from Abrahamsson (1966Abrahamsson ( , 1971). Noro and Buckup (2008) studied Parameters for the life history of A. astaci were aggregated from Strand et al. (2012) and Oidtmann et al. (2002). Values for the infection rate for susceptible host were adapted from A. astacus data from Makkonen et al. (2014). The survival of A. astaci spores has not been studied in detail in natural conditions and may vary considerably (Svoboda et al., 2017). We assume that the half-life of A. astaci spores is in between the estimated extremes, 14 days.
The decay of carcasses occurs in aquatic environment: carrions become edible at rate γ T , and the decay of the infective spores from the infected carcasses occurs at rate γ C . In the latter process, the infected carcasses turn into uninfective carcasses. The decay process describing the general removal of the carcasses from the environment, γ T , depends on the environment as it happens through the biological decomposing process and as a consequence of scavenging by other animals. Data of the decay processes in the aquatic environments are scarce. Parmenter and Lamarra (1991) observed that 80% of the total dry mass of fish was decomposed in the period of 4.5 months in a freshwater marsh environment. The carcasses were protected from scavengers, and thus, we consider γ T = 0.01. The decay of the disease has been suggested to be a quicker process. Oidtmann et al. (2002)

| Numerical methods
The numerical simulations of the model (1)

| RE SULTS
In the absence of the plague, the crayfish population dynamics are locally stable. For the given rate of cannibalism, c = 1 × 10 −5 the equilibrium susceptible adult population size settles down to the level S = 4320, and the ratio of the juveniles to the adults is J/S = 0.41.

| Effects of environmental transmission compared to other transmission routes
The coexistence dynamics between the crayfish and plague are locally stable when the environmental transmission rate α is low (Figure 2a), as is indicated by the area where peak-to-peak amplitude is zero. An increase in the environmental transmission rate turns the coexistence dynamics into heavy periodic oscillations (Figure 2a). At the same time, the minimum values of the crayfish population fluctuations decrease close to a local extinction (Figure 2b). Thus, a high environmental transmission rate prevents stable coexistence of the crayfish and the oomycete, but cyclic coexistence with population fluctuations is common. The contact infections strengthen the epidemic notably only if the environmental infection rate, α, is low (Figures 3a,b and 4).
The infections from the environment have a major role in increasing disease epidemics ( Figure 5). Environmental transmission    (Figure 5d).

| Effects of scavenging without environmental transmission
When we consider the effects of increasing rates of contact transmission and scavenging but keeping the environmental transmission almost absent (α = 1 × 10 −12 ), we observe a disease-free susceptible population at low contact transmission rate (b = 0;   and already at α = 1 × 10 −9 the difference is less than 10%.

| Effects of cannibalism
F I G U R E 3 (a) the coexistence dynamics of the crayfish and the disease remain stable when the environmental transmission rate α is low. When the environmental transmission rate increases the coexistence dynamics turn abruptly into notable periodic oscillations. Y-axis shows the amplitude of the periodic oscillations of the susceptible crayfish population. Y-value of 0 means either that the crayfish population reaches a stable state, or the population goes extinct. (b) the minimum values of the oscillations decrease close to extinction with increasing the environmental transmission rate α. Y-axis is log10 scaled to present a better view of the uneven gradient.
When the environmental infection rate, α, increases it soon takes over the regulation of the population driving the mean size to a very low level (Figure 8a). If cannibalism rate is low, the dynamics are cyclic. Increasing cannibalism rate stabilizes the dynamics, higher α requiring higher cannibalism rate for the effect.
When the environmental transmission rate is zero, the respective incidence rate is obviously zero as well (Figure 9a). Increasing environmental transmission rate increases, however, the corresponding incidence rate until a possible extinction. Low rate of cannibalism together with high rate of environmental transmission

F I G U R E 6
The mean population sizes of the susceptible and infected adult crayfish when the environmental infection rate is low (α = 1 × 10 −12 ). Increasing contact transmission rate decreases the susceptible (a) and infected (b) crayfish population mean sizes. Scavenging has notable effect only when contact transmission rate is low, but higher than zero.
causes slow periodic oscillations (Figure 9a). The incidence rates due to the contact infections ( Figure 9b) and transmission through scavenging (Figure 9c) reach the highest peak when the environmental infection rate is zero and the cannibalistic infection rate is minimum (c = 1 × 10 −6 ). Both decrease quickly with either increasing environmental infection rate or increasing cannibalistic infection rate.

| DISCUSS ION
Environmental transmission including transmission through water and surfaces forms a natural route for the pathogen (Oidtmann et al., 2002). According to our model, environmental transmission is the decisive mechanism in the development of disease epidemics.
Compared with a pathogen-free population, a low environmental transmission rate decreases the crayfish population size, but only with a low risk of extinction, regardless of the contact transmission rate. Higher environmental transmission rate, however, substantially increases the number of infected crayfish, potentially driving both the crayfish and pathogen populations to extinction. On the other hand, high contact transmission rate creates probability for cyclic population fluctuations with low mean population size, though the dynamics are strongly dependent on the initial size of the infected population. As a result, a high contact transmission rate with a low but nonzero environmental transmission rate can lead to extinction, cyclic population with a minimum close to extinction, or large susceptible crayfish population. In accordance with our model, A. astaci has been reported to survive even years after an outbreak within a low-density crayfish population (Viljamaa-Dirks et al., 2011).
In natural conditions, the relative importance of environmental and contact infections could depend on the habitat complexity so that contact infections might dominate in environments where the F I G U R E 7 The incidence rates of the different infection routes of the plague when the environmental infection rate is low. (a) Environmental infection; (b) infections through contacts; (c) infections through scavenging; (d) infections through cannibalism. Incidence rate through scavenging increases with increasing scavenging rate. The effect of scavenging rate on the other incidence rates are most visible when contact transmission rate remains low, but above zero.

F I G U R E 8
Mean population sizes of the (a) susceptible and (b) infected adult crayfish as a function of the environmental infection rate, α, and the infection rate through cannibalism, c. α and c have strong interaction, c acting as a stabilizing force. In the absence of environmental transmission, high rate of cannibalism can eradicate the pathogen from the system. However, even weak environmental transmission prevents the pathogens extinction.
crayfish distribution is very patchy. Thus, they may not be biologically irrelevant but induce dynamics that do not obey standard densitydependent theory as suggested by our model at low environmental transmission rates.

Environment remained the most obvious transmission route for
A. astaci in most scenarios included in our simulations. However, Cerenius and Söderhäll (1984) reported that in turbulent water, A. astaci spores formed cysts that are inactive but long lived and can transform back to infectious spores. Therefore, high water turnover, as in fast flowing streams, could decrease the importance of environmental transmission. Similarly, in initial stage of an outbreak, the spore density in water is low (Strand et al., 2014). This is plausible because A. astaci produces motile zoospores at the fastest rate during the time right before and a few days after the death of the host. The competition for the carcasses between scavenger species can be strong, while the decomposition process is relatively fast in submerged carcasses (Anderson et al., 2019;Beasley et al., 2012;Fenoglio et al., 2014). Therefore, the effective scavenging time for the crayfish carcasses is limited, which affects the efficiency of carcasses as infection sources. However, empirical data on the process are scarce and urgently needed. Consequently, the significance and the action of intraspecific necrophagy as a part of population dynamics are currently not thoroughly understood.
In the present model, cannibalism stabilizes the host population dynamics by reducing the amplitude of the population cycles.
Cannibalism can also slow down the epidemic by two mechanisms.
First, the attacker removes the infection transmitter from the system, thus decreasing the contact infections. Second, by removing the diseased individuals before they reach the state where A. astaci spore production is at its highest, cannibalism reduces the effect of the environmental transmission. Therefore, the effect of cannibalism on the population is positive, even though it repeats the cycle of transmission. Importantly, increasing cannibalism can eradicate the oomycete completely if the environmental transmission rate is very low. This suggests a role for evolutionary group selection such that cannibalistic groups could be more efficient in resisting diseases than non-cannibalistic groups. However, the feasibility of this hypothesis would require further analysis and testing. Abrahamsson (1966) suggested that a crayfish population can be regulated by cannibalism of large males. This hypothesis was supported by Houghton et al. (2017), who verified in P. leniusculus that cannibalizing individuals were primarily notably larger than the victims. To our knowledge, the population dynamical consequences of this have not been studied theoretically. Polis (1981) names intraspecific predation as a homeostatic factor possibly F I G U R E 9 Incidence rates of the infections due to (a) environment, (b) contacts, (c) scavenging, and (d) cannibalism. Notice the different view angle in subfigure (d). In subfigure (a), one can see the stabilizing effect of increasing the rate of cannibalism, where at high environmental transmission rate the mean incidence rate is unstable at the area of low cannibalism rate. Subfigure (d) shows the strong interaction between the environmental transmission rate and the rate of cannibalism.
influencing population structure, life history, competition for mates and resources, and other behavior, among many animals. In his review (see also Fox, 1975), he mentions that cannibalism occurs in (at least in) about 1300 species. In our simple model, cannibalism limits the population growth such that population size declines with increasing intensity of intraspecific predation and population size is always stable over time. No other density-dependent selfregulating factors are needed to maintain stable population size (Rudolf & Antonovics, 2007). In size-structured models with densitydependent recruitment, also other types of solutions (cyclic dynamics) are possible. Because our model did not have carrying capacity or density-dependent recruitment, the modeled two contradictory processes necessarily lead to a stable equilibrium in a disease-free system.
When A. astaci is introduced to the system, be it through nonindigenous crayfish, digestive tract of fish, contaminated equipment, or infected pieces of crayfish carcasses, its transmission modes are versatile (Oidtmann et al., 2002;Svoboda et al., 2017). Therefore, the epidemiological model needs to extend the classical SI model with both environmental and vector borne transmissions (Anderson & May, 1981 (Jussila et al., , 2015. The resistance against the pathogen in North American crayfish can be attributed to coevolution between the crayfish and the endemic pathogen (Svoboda et al., 2017). Elevated mortality (Aydin et al., 2013;Thomas et al., 2020) and declined fecundity due to eroded swimmeret syndrome caused by chronic infection in some European signal crayfish populations (Jussila et al., 2017)  incorporate the potential environmental transmission through reservoir species, but the epidemics rely heavily on the transmission through the frequency-based contacts with dead individuals. ASF has been modeled using purely density-dependent contact infection model (Barongo et al., 2016), but the disease dynamics can be modeled with several transmission routes similarly to the crayfish plague (O'Neill et al., 2020). Transmission routes are similar to crayfish plague, including contact and environmental infections.
Cannibalism has also been shown to be part of the ASF dynamics (Cukor et al., 2020), though not as a population regulator. In the EVD epidemic, the transmission through the dead was caused by the tradition of touching the deceased as a part of burial ceremonies. The tradition, which is present in many human cultures, was an important transmission route during the West African Ebola epidemic (Manguvo & Mafuvadze, 2015). Veijo Kaitala: Conceptualization (equal); formal analysis (lead); investigation (equal); supervision (lead); visualization (lead); writing -original draft (equal); writing -review and editing (equal).

ACK N OWLED G M ENTS
We memorialize the late Jouni Laakso for his inspiration to this work.
During the preparation of this manuscript, RK was financially supported by Nordic Centre of Excellence for Sustainable and Resilient Aquatic Production SUREAQUA.

CO N FLI C T O F I NTE R E S T
We declare no conflict of interest.

DATA AVA I L A B I L I T Y S TAT E M E N T
Data sharing not applicable to this article as no datasets were generated or analysed during the current study.